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annotate scripts/linear-algebra/rank.m @ 7016:93c65f2a5668

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[project @ 2007-10-12 06:40:56 by jwe]
author jwe
date Fri, 12 Oct 2007 06:41:26 +0000
parents 34f96dd5441b
children a1dbe9d80eee
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1 ## Copyright (C) 1996, 1997 John W. Eaton
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2 ##
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3 ## This file is part of Octave.
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4 ##
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5 ## Octave is free software; you can redistribute it and/or modify it
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6 ## under the terms of the GNU General Public License as published by
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7 ## the Free Software Foundation; either version 3 of the License, or (at
93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe]
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8 ## your option) any later version.
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9 ##
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10 ## Octave is distributed in the hope that it will be useful, but
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11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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13 ## General Public License for more details.
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14 ##
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15 ## You should have received a copy of the GNU General Public License
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16 ## along with Octave; see the file COPYING. If not, see
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17 ## <http://www.gnu.org/licenses/>.
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18
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19 ## -*- texinfo -*-
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20 ## @deftypefn {Function File} {} rank (@var{a}, @var{tol})
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21 ## Compute the rank of @var{a}, using the singular value decomposition.
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22 ## The rank is taken to be the number of singular values of @var{a} that
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23 ## are greater than the specified tolerance @var{tol}. If the second
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24 ## argument is omitted, it is taken to be
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25 ##
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26 ## @example
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27 ## tol = max (size (@var{a})) * sigma(1) * eps;
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28 ## @end example
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29 ##
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30 ## @noindent
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31 ## where @code{eps} is machine precision and @code{sigma(1)} is the largest
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32 ## singular value of @var{a}.
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33 ## @end deftypefn
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35 ## Author: jwe
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36
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37 function retval = rank (A, tol)
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39 if (nargin == 1)
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40 sigma = svd (A);
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41 if (isempty (sigma))
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42 tolerance = 0;
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43 else
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44 tolerance = max (size (A)) * sigma (1) * eps;
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45 endif
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46 elseif (nargin == 2)
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47 sigma = svd (A);
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48 tolerance = tol;
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49 else
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50 print_usage ();
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51 endif
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52
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53 retval = sum (sigma > tolerance);
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54
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55 endfunction